Use of Exchangeable Pairs in the Analysis of Simulations

The method of exchangeable pairs has emerged as an important tool in proving limit theorems for Poisson, normal and other classical approximations. Here the method is used in a simulation context. We estimate transition probabilitites from the simulations and use these to reduce variances. Exchangeable pairs are used as control variates. Finally, a general approximation theorem is developed that can be complemented by simualtions to provide actual estimates of approximation errors.